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The Classification of Two-Particle Spin States and Bell–CHSH Inequalities for Mixed States

Vladimir I. Man’ko, V. A. Andreev

Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20040 citations

The Reduction of Density Matrix and Measurement of Bell-CHSH Inequalities

V. A. Andreev

The right hand side of Bell inequalities don’t depend on a form of any two‐particle spin state. In the case of the generalized Bell‐Clauser‐Horne‐Schimony‐Holt inequalities the right hand side depend on a form of concrete two‐particle state. The left hand sides of these inequalities depend on four arbitrary vectors defined in three‐dimensional space. They define directions on which spins of particles forming a correlated pair are projected. Our aim is to find such vectors that left‐hand side of the inequality should takes its maximum value. In other words on these vectors the inequality transforms into equality. It is shown that it can be done with the help of special reduction of density matrix of two‐state spin state.The right hand side of Bell inequalities don’t depend on a form of any two‐particle spin state. In the case of the generalized Bell‐Clauser‐Horne‐Schimony‐Holt inequalities the right hand side depend on a form of concrete two‐particle state. The left hand sides of these inequalities depend on four arbitrary vectors defined in three‐dimensional space. They define directions on which spins of particles forming a correlated pair are projected. Our aim is to find such vectors that left‐hand side of the inequality should takes its maximum value. In other words on these vectors the inequality transforms into equality. It is shown that it can be done with the help of special reduction of density matrix of two‐state spin state.

AIP conference proceedingsJan 1, 20070 citations

A closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality

Rajarshi Pal, Sibasish Ghosh A

In this note, we discuss a closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality. This is then used to numerically compute the relative volume of states showing hidden Bell-CHSH non-locality , among all two-qubit states with one-sided reduction maximally mixed.

arXiv:1410.7574Oct 28, 20141 citation

Reduction of the Density Matrix and Generalized Bell Inequalities

V. A. Andreev

Acta Physica Hungarica A) Heavy Ion PhysicsNov 1, 20061 citation

Unruh-De Witt detectors, Bell-CHSH inequality and Tomita-Takesaki theory

F. M. Guedes, M. S. Guimarães, I. Roditi +1 more

A bstract The interaction between Unruh-De Witt spin 1/2 detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.A bstract The interaction between Unruh-De Witt spin 1/2 detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.

arXiv:2401.03313Journal of High Energy PhysicsJun 6, 20247 citations

THE STRUCTURE OF THE DENSITY MATRIX FOR PARTICLES OF HIGHER SPIN VALUES

W. Konar

Jan 1, 19650 citations

Reduction of the two-spin state density matrix and evaluation of the left-hand side of the Bell-CHSH inequality

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Reduction of the two-spin state density matrix and evaluation of the left-hand side of the Bell-CHSH inequality

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